Backing up a truck-trailer with suboptimal distance trajectories

In this paper, a fuzzy logic controller is designed for back-driving a truck-trailer model into a prescribed parking lot along a suboptimal trajectory where the optimality is defined in terms of the natural parabolic driving paths that a truck-trailer travels. By applying fuzzy logic control techniques, a controller is developed with nine rules, which works well even without using a mathematical model of the truck-trailer system. As long as the states of the truck are measurable at each discrete-time step during the control process, this controller can drive the truck-trailer to follow any feasible trajectories, and to park successfully into the lot along a suboptimal trajectory. In addition to the design, controllability and stability of the control system are discussed, by using the small gain theorem for the truck-trailer system and the Lyapunov method for the single truck system. Simulation results are presented to demonstrate the accuracy and effectiveness of the new fuzzy logic controller, and to compare its control performance with other fuzzy logic controllers that were designed for the same purpose under the similar conditions without using any optimality criterion.